Question:
Find the equation of the tangent and the normal to the following curves at the indicated points:
$y=x^{2}$ at $(0,0)$
Solution:
finding the slope of the tangent by differentiating the curve
$\frac{\mathrm{dy}}{\mathrm{dx}}=2 \mathrm{x}$
$\mathrm{m}($ tangent $)$ at $(\mathrm{x}=0)=0$
normal is perpendicular to tangent so, $m_{1} m_{2}=-1$
$\mathrm{m}$ (normal) at $(\mathrm{x}=0)=\frac{1}{0}$
We can see that the slope of normal is not defined
equation of tangent is given by $y-y_{1}=m$ (tangent) $\left(x-x_{1}\right)$
$y=0$
equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$
$x=0$